Summary: Coercive Subtyping in Lambda­Free Logical
Frameworks
Robin Adams
robin@cs.rhul.ac.uk
Royal Holloway, University of London
Abstract. Coercive subtyping is a powerful approach to subtyping in
dependent type theories, but its theoretical properties are often di#­
cult to prove. Lambda­free logical frameworks such as TF have shown
themselves to be a powerful tool for investigating the theory of logical
frameworks, thanks to the close correspondance between a lambda­free
frame and a traditional framework such as LF. We show how a type
theory with coercive subtyping may be defined within TF. An operation
of typecasting plays the role that coercive application plays in LF. We
show that the resulting systems in TF and LF are equivalent, and how
several results may be proven more easily in TF and then lifted to LF.
Keywords: Coercive subtyping, logical frameworks, lambda­free logical
frameworks, coercive application, typecasting
1 Introduction
When working with dependent type theories, we often find it convenient to
introduce a notion of subtyping. Intuitively, to say the type A is a subtype of the